We present an approach to simulate divide-and-conquer algorithms in a space-efficient way, and illustrate it by giving space-efficient algorithms for the closest-pair, bichromatic closest-pair, all-nearest-neighbors, and orthogonal line segment intersection problems.

Abstract. Finding the fastest algorithm to solve a problem is one of the main issues in Computational Geometry. Focusing only on worst case analysis or asymptotic computations leads to the development of complex data structures or hard to implement algorithms. Randomized algorithms appear in this scenario as a very useful tool in order to obtain easier implementations within a good expected time bound. However, parallel implementations of these algorithms are hard to develop and require an in-depth understanding of the language, the compiler and the underlying parallel computer architecture. In this paper we show how we can use speculative parallelization techniques to execute in parallel iterative algorithms such as randomized incremental constructions. In this paper we focus on the convex hull problem, and show that, using our speculative parallelization engine, the sequential algorithm can be automatically executed in parallel, obtaining speedups with as little as four processors, and reaching 5.15x speedup with 28 processors. 1